NNLO Logarithmic Expansions and High Precision Determinations of the QCD background at the LHC: The case of the Z resonance

TL;DR

This paper reviews advanced NNLO QCD methods for solving the DGLAP equation, focusing on their impact on high-precision background predictions at the LHC, especially near the Z resonance.

Contribution

It introduces a recursive x-space approach for NNLO evolution, including resummation techniques, and analyzes their numerical differences and effects on Z resonance predictions.

Findings

NNLO evolution reduces the Drell-Yan cross section compared to NLO.

Differences between evolution schemes are numerically significant.

The approach can be extended to Z' searches.

Abstract

New methods of solutions of the DGLAP equation and their implementation through NNLO in QCD are briefly reviewed. We organize the perturbative expansion that describes in $x$-space the evolved parton distributions in terms of scale invariant functions, which are determined recursively, and logarithms of the ratio of the running couplings at the initial and final evolution scales. Resummed solutions are constructed within the same approach and involve logarithms of more complex functions, which are given in the non-singlet case. Differences in the evolution schemes are shown to be numerically sizeable and intrinsic to perturbation theory. We illustrate these points in the case of Drell-Yan lepton pair production near the Z resonance, analysis that can be extended to searches of extra $Z^{\prime}$. We show that the reduction of the NNLO cross section compared to the NLO prediction may be attributed to the NNLO evolution.